Research

Ecological dynamics and the basis for sympatric phenotypic diversification

Stability and complexity in eco-evolutionary model systems

It is well-known that demographic stochasticity can give rise to regular and persistent population cycles in simple consumer-resource models that are deterministically stable. The existence of these, so-called quasi-cycles, substantially expands the scope for natural patterns of periodic population oscillations caused by ecological interactions, thereby complicating the conclusive interpretation of such patterns. I have previously shown, however, that it is both feasible and straightforward to accurately distinguish between these two types of cycles using a combination of statistical methods from time series analysis. Using data from real ecological time series of lynx, snowshoe hare, sea otter, and wolverine populations, I demonstrated that even short and imperfect time series allow quasi-cycles and deterministic limit-cycles to be reliably distinguished (Pineda-Krch et al., 2007).

The ecological and evolutionary significance of different types of population cycles remains unclear, however, and addressing this topic is of particular importance as the majority of evolutionary models assume that populations are at demographic equilibrium as the evolutionary dynamics unfolds. In reality, of course, it is possible to envision that evolving quantitative traits may move the population between dynamical regimes in parameter space and change the stability properties of the population as it evolves. My aim is to explore the role of different types of population fluctuations (i.e. quasi-cycles, limit cycles, environmental forcing) on the evolutionary dynamics and vice versa, i.e. the feedback from evolutionary dynamics to ecological dynamics.

The role of phenotypic plasticity in diversification and speciation

An increasing number of studies show phenotypic evidence in support of sympatric speciation. However, when a population has undergone a branching in its phenotype, is this due to evolutionary branching in the underlying genotype or to phenotypic plasticity modifying a single genotype? In this project I am using a eco-evolutionary model system to study the conditions under which a phenotype experiencing selection for alternative optimal phenotypes gives rise to either genetically based phenotypic branching or to phenotypic plasticity. Using a Rosenzweig-MacArthur predator-prey model where the predator is experiencing selection for two mutually exclusive phenotypes I have previously show that populations undergoing high amplitude fluctuations tend to evolve phenotypic plasticity whereas populations with more stable numerical dynamics lose their plasticity and undergo adaptive branching into two incipient species (Svanbäck, Pineda-Krch & Doebeli, 2009). This result is of fundamental importance for increasing our understanding of the ecological conditions under which adaptation and speciation occurs.

My goal for the future is to explore how ecological dynamics influence the coevolution of predator-prey populations, i.e. if both predator and prey are evolving how does this affect the evolutionary outcome (i.e. evolutionary branching vs. increased phenotypic plasticity). Yet another topic I am exploring (building on Hellmann & Pineda-Krch, 2007) is how selection on two (or more) genetically correlated traits affects the evolutionary outcome and how this relates to the underlying ecological dynamics.

Phenology and evolutionary dynamics

Recently I started a project addressing the role of phenology (the timing of periodic life cycle events, e.g. flowering time, timing of spring arrival of migratory birds, timing of breeding period, etc.) on evolutionary dynamics. While there is an extensive literature addressing the evolution of phenologies as well as the effect of global climate change on phenology the fundamental question of how phenology affects evolutionary dynamics has received little attention. For example, in continuous-time eco-evolutionary models (e.g. those based on the theory of Adaptive Dynamics) it is typically assumed that vital processes such as birth and reproduction occur continuously throughout the season. My aim is to explore the evolutionary consequences of pulsed life cycle events, e.g. breeding only occurring during at specific time of the year. Currently I am exploring this topic using a simple Logistic growth eco-evolutionary model with pulsed reproduction. In its original version (see e.g. Doebeli & Dieckmann, 1999) birth is continuous and sympatic speciation occurs as a result of competition for resources. Preliminary results from my version of the model suggest that the pulsed reproduction rapidly drive the population to a fitness minimum at the verge of adaptive branching, but without actually undergoing speciation. This result is particularly interesting in light of the climate warming trend that the world experiencing. For many populations this is resulting in a longer breeding seasons and the results from the model suggest that an increase in the duration of the yearly reproductive pulse could result in a sudden and rapid evolutionary diversification.

I anticipate to explore this topic extensively over the next few years using more complex consumer-resource and host-pathogen models for different ecological systems and phenology traits.

Predictive modelling of forest insect dynamics across spatial and temporal scales

In order to manage and control outbreaks of damaging forest insect populations one has to be able to predict the location and time of future outbreaks. In this project I am developing a statistical framework, based on a spatially explicit Markov process logistic regression model, for predicting the location and time of outbreaks over large spatial areas. The overarching goal of this project is to develop a model that is simple to implement and that maximizes predictive accuracy over large spatial regions by integrating ecological, climatic, and topographical information.

I am currently validating the model by using Mountain pine beetle outbreak data for British Columbia (Canada) to determine the historical outbreak probability. This work has shown that the model performs well  and hence can be used to determine high outbreak risk regions for control and management. At present, I am also working on extending the model by incorporating long distance dispersal, process-based formulations of ecological processes such as host regeneration, and improving the predictions under global climate change scenarios. Along with Mark Lewis (University of Alberta) and Andrew Liebhold (USDA Forest Service), I have organized a working group at NIMBioS to explore these issues in greater detail.

Algorithms for stochastic dynamics of continuous time ecological and evolutionary processes

Because analytical solutions to stochastic time-evolution equations for all but the simplest systems are intractable, while numerical solutions are often prohibitively difficult, stochastic simulations have become an invaluable tool for studying the dynamics of ecological systems with finite population size. My goal in this project is to develop efficient computational algorithms for stochastic simulations of ecological and evolutionary processes in continuous time. As part of this project, I have developed the package GillespieSSA for the statistical computing language R, implementing the stochastic simulation algorithm by Gillespie. This package provides a simple-to-use and extensible interface to several existing and new stochastic simulation algorithms for generating simulated trajectories of finite population continuous-time models (Pineda-Krch, 2008). Using this class of algorithms to study the evolutionary dynamics of quantitative traits poses challenges due to the infinite size of trait space. Under the auspices of this project I am pursuing several lines of work, including further development of the GillespieSSA package, and the development of novel algorithms suitable for simulating the time-evolution of quantitative traits.

My research make use of the computational infrastructure and resources of CMB (Centre for Mathematical Biology), AICT (Academic Information and Communication Technologies) of the University of Alberta, WestGrid (Western Canada Research Grid), and SHARCNET.